MATLAB implementation of hp finite elements on rectangles
Alexej Moskovka, Jan Valdman
TL;DR
This paper presents a MATLAB implementation of hierarchical hp finite elements on rectangles, facilitating efficient assembly of matrices and solution approximation for boundary value problems with variable refinements.
Contribution
It introduces a simple MATLAB code for hierarchical shape functions on rectangles, enabling effective p-refinement and matrix assembly in finite element analysis.
Findings
Efficient assembly of mass and stiffness matrices with hierarchical structure
Successful approximation of boundary value problems with various h and p refinements
Implementation available for download and practical use
Abstract
A simple MATLAB implementation of hierarchical shape functions on 2D rectangles is explained and available for download. Global shape functions are ordered for a given polynomial degree according to the indices of the nodes, edges, or elements to which they belong. For a uniform p-refinement, the hierarchical structure enables an effective assembly of mass and stiffness matrices. A solution of a boundary value problem is approximated for various levels of uniform h and p refinements.
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Taxonomy
TopicsMetal Forming Simulation Techniques · Composite Material Mechanics · Advanced Numerical Methods in Computational Mathematics